DP - Counting coin change

Question

The problem requires to count number of coin changes for a particular cost.

For example, if I have coin values of 50, 20, 10, 5, 1, I can form costs of:

5 => (5), (11111), which are 2 ways.

10 => (10), (5, 5), (5, 11111), (11111, 11111), which are 4 ways.

Here is my function. It is returning wrong results begging from cost of 10 (returns 9 ways while the actual number of ways is only 4)

int dp[10000];
int coins[] = { 50, 20, 10, 5, 1 };
int rec(int n)
{
  if (n == 0) return 1;
  if (dp[n] != -1) return dp[n];
  int cnt = 0;
  for (int i = 0; i < 5; i++)
    if (coins[i] <= n) cnt += rec(n - coins[i]);
  return dp[n] = cnt;
}

How can I fix this function to give the correct number of ways? Is this algorithm correct even? see the complete code and its output here

NOTE: my problem is not with dp array initialization. I am using memset to initialize it to -1 each time before calling rec.

What is the problem exactly (what do you _want_ to get, and what do you _actually_ get)? — SingerOfTheFall, Aug 08 '12 at 08:59

score 3 · Accepted Answer · answered Aug 08 '12 at 09:17

3

(5, 1, 1, 1, 1, 1) and (1, 1, 1, 5, 1, 1) is different way in you algorithm, you should keep it decreasing.

int dp[10000][5];  // dp[20][2] means, if the biggest coin is coins[2],
                   // how much ways for 20 ?
int coins[] = { 1, 5, 10, 20, 50 }; // here
int rec(int n, int m)
{
  int cnt = 0;
  int i;
  if (n == 0) return 1;
  //if (m == 0) return 1;
  if (dp[n][m] != -1) return dp[n][m];
  for (i = 0; i <= m; i++)
    if (coins[i] <= n) cnt += rec(n - coins[i], i);
  return dp[n][m] = cnt;
}

int main()
{
        memset(dp, -1, sizeof(dp));
        printf("%d\n", rec(10, 4));
}

answered Aug 08 '12 at 09:17

Lai Jiangshan

1,420
1
13
23

Why did you call it with `m = 4` ? – Aug 08 '12 at 09:22
3

He exchanged the order. He made the coins go from smallest to highest, and the for loop from 0 to m, so its the same as mine, just differently formatted... – SinisterMJ Aug 08 '12 at 09:23
@Lai it is not different. I am sorry I forgot to indicate so. The algorithm requires to count ***distinct*** ways. – Aug 08 '12 at 09:26

score 1 · Answer 2 · answered Aug 08 '12 at 09:08

1

The result is wrong since you never make sure that your algorithm starts with the 5 coin. (5,11111) is just as valid in your code as (1, 5, 1111), but this is the same result. Your result should be wrong from 6 and higher, not 10 and higher.

To fix this you can do like a cutoff in your function rec():

int rec(int n, int cutoff)
{
  if (n == 0) return 1;
  if (dp[n] != -1) return dp[n];
  int cnt = 0;
  for (int i = cutoff; i < 5; i++)
    if (coins[i] <= n) cnt += rec(n - coins[i], i);
  return dp[n] = cnt;
}

Should do it.

Edit: you will have to take care of your dp[] array, since it does not care about this cutoff, but this in general is the fault you are running into. You could comment that line, and check if this works.

answered Aug 08 '12 at 09:08

SinisterMJ

3,425
2
33
53

So how to call it with n = 10 for example? – Aug 08 '12 at 09:10
The first call will have to be with rec(10, 0). I have edited that your dp[] array will screw up that algorithm, so just to make sure the idea works, you should comment the line if(dp[n]!=-1)... – SinisterMJ Aug 08 '12 at 09:12
1

Sould I make `dp` two dimensional to use cutoff? It doesn't work when taking off the comment – Aug 08 '12 at 09:16
Yes, that would be the fix for that. The second element should show the maximum number allowed. Would be something like Lai wrote, I just wanted to show where the error was coming from. – SinisterMJ Aug 08 '12 at 09:24

score 1 · Answer 3 · answered Aug 08 '12 at 09:12

One remark: Your initialization

memset(dp, -1, sizeof dp);

is not really safe. memset initializes every byte of a memory space (see http://www.cplusplus.com/reference/clibrary/cstring/memset/.). For this particular case you are lucky and the representation of int(-1) is (probably) the same of four times unsigned char(-1).

I would suggest using std::fill ( http://www.cplusplus.com/reference/algorithm/fill/ ).

DP - Counting coin change

3 Answers3

Linked